Is it advisable not to get involved with a girl who has had breast cancer before for health reasons?

No risk to you! 1 in 8 women get breast cancer. If your partner has had breast cancer, there is no health risk to you. Women who have had breast cancer have strength, insight and perspective that other women may not have. But if you are not ready to love someone in sickness and in health, and support that person through something like cancer, you aren't ready for a serious relationship.
Not Contagious. One misconception is that cancer is contagious. This is false. There are no health related reasons one can not have a meaningful and serious relationship with a cancer survivor.
Only you can answer. Following treatment, the chance of breast cancer returning is quite variable but always a risk. Many of my cancer patients tell me that living with this risk is more difficult than the treatment they endured. Cancer survivors need a very strong support system; if you are not up to that challenge, it is best to answer that now.

Related Questions

Without any family past, how common is breast cancer in a teen girl, and what are signs/symptoms?

Very rare. Without family history, you should not be concerned about breast cancer at your age. You may consult this site for more information on this topic.

Is it actually ok for a girl to be taking birth control pills if her mother had breast cancer?

Yes. Not all breast cancers are hereditary or with receptors to hormones. Because you are younger, the risk is smaller. But keep in mind, your risk for breast ca is higher than the population. My suggestion is cont with the pill but do monthly self breast checks and do your mammogram every 2 yrs if the history is birads 1 or 2.